Question

The molar specific heats of an ideal gas at constant pressure and volume are denoted by $C_p$ and $C_v$ respectively. If $\gamma =\frac{C_p}{C_v}$ and R is the universal gas constant, then $C_v$ is equal to :

• A. $\frac{1+\gamma }{1-\gamma }$
• B. $\frac{R}{(\gamma -1)}$
• C. $\frac{(\gamma -1)}{R}$
• D. $\gamma R$

Answer 1

Answer: (B)

$\frac{R}{(\gamma -1)}$

We know that,
$C_P-C_V$ = $R$
Also, $\gamma =\frac{C_P}{C_V}$
From the given correlations, we get $C_V$ = $\frac{R}{(\gamma -1)}$